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R Software Module

rwasp_Two Factor ANOVA.wasp

Title produced by software

Two-Way ANOVA

Date of computation

Thu, 20 Dec 2012 16:42:44 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/20/t1356039798ki3z48kq5hbwqt5.htm/, Retrieved Thu, 18 Apr 2024 14:32:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203152, Retrieved Thu, 18 Apr 2024 14:32:45 +0000

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Estimated Impact

102

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Paper chi-squared...] [2012-12-18 12:06:51] [33fe548a21de6aef2b38519618b03303]
-       [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [rfc chi kwadraat ...] [2012-12-19 22:20:44] [5681f3f0ac2340d6f296c6f0abf509cb]
- RMPD    [Two-Way ANOVA] [RFC anova deel 5] [2012-12-20 20:06:44] [5681f3f0ac2340d6f296c6f0abf509cb]
- R P         [Two-Way ANOVA] [anova deel 5 rfc] [2012-12-20 21:42:44] [b8d3d7c3406b9c8dc9154eb4f7d497b9] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203152&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203152&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203152&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	0.15	-0.15	0.043	-0.043

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
Response ~ Treatment_A * Treatment_B \tabularnewline
means & 0.15 & -0.15 & 0.043 & -0.043 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203152&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]Response ~ Treatment_A * Treatment_B[/C][/ROW]
[ROW][C]means[/C][C]0.15[/C][C]-0.15[/C][C]0.043[/C][C]-0.043[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203152&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203152&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

ANOVA Model
Response ~ Treatment_A * Treatment_B
means	0.15	-0.15	0.043	-0.043

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	1
Treatment_A	1	0.426	0.426	3.352	0.069
Treatment_B	1	0.056	0.056	0.443	0.507
Treatment_A:Treatment_B	1	0.005	0.005	0.041	0.84
Residuals	150	19.077	0.127

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
 & 1 &  &  &  &  \tabularnewline
Treatment_A & 1 & 0.426 & 0.426 & 3.352 & 0.069 \tabularnewline
Treatment_B & 1 & 0.056 & 0.056 & 0.443 & 0.507 \tabularnewline
Treatment_A:Treatment_B & 1 & 0.005 & 0.005 & 0.041 & 0.84 \tabularnewline
Residuals & 150 & 19.077 & 0.127 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203152&T=2

[TABLE]
[ROW][C]ANOVA Statistics[/C][/ROW]
[ROW][C] [/C][C]Df[/C][C]Sum Sq[/C][C]Mean Sq[/C][C]F value[/C][C]Pr(>F)[/C][/ROW]
[ROW][C][/C][C]1[/C][C][/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Treatment_A[/C][C]1[/C][C]0.426[/C][C]0.426[/C][C]3.352[/C][C]0.069[/C][/ROW]
[ROW][C]Treatment_B[/C][C]1[/C][C]0.056[/C][C]0.056[/C][C]0.443[/C][C]0.507[/C][/ROW]
[ROW][C]Treatment_A:Treatment_B[/C][C]1[/C][C]0.005[/C][C]0.005[/C][C]0.041[/C][C]0.84[/C][/ROW]
[ROW][C]Residuals[/C][C]150[/C][C]19.077[/C][C]0.127[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203152&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203152&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

ANOVA Statistics
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
	1
Treatment_A	1	0.426	0.426	3.352	0.069
Treatment_B	1	0.056	0.056	0.443	0.507
Treatment_A:Treatment_B	1	0.005	0.005	0.041	0.84
Residuals	150	19.077	0.127

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
1-0	-0.168	-0.349	0.013	0.069
1-0	0.039	-0.077	0.155	0.51
1:0-0:0	-0.15	-0.427	0.127	0.497
0:1-0:0	0.043	-0.118	0.204	0.899
1:1-0:0	-0.15	-0.625	0.325	0.844
0:1-1:0	0.193	-0.092	0.478	0.296
1:1-1:0	0	-0.53	0.53	1
1:1-0:1	-0.193	-0.672	0.286	0.723

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
1-0 & -0.168 & -0.349 & 0.013 & 0.069 \tabularnewline
1-0 & 0.039 & -0.077 & 0.155 & 0.51 \tabularnewline
1:0-0:0 & -0.15 & -0.427 & 0.127 & 0.497 \tabularnewline
0:1-0:0 & 0.043 & -0.118 & 0.204 & 0.899 \tabularnewline
1:1-0:0 & -0.15 & -0.625 & 0.325 & 0.844 \tabularnewline
0:1-1:0 & 0.193 & -0.092 & 0.478 & 0.296 \tabularnewline
1:1-1:0 & 0 & -0.53 & 0.53 & 1 \tabularnewline
1:1-0:1 & -0.193 & -0.672 & 0.286 & 0.723 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203152&T=3

[TABLE]
[ROW][C]Tukey Honest Significant Difference Comparisons[/C][/ROW]
[ROW][C] [/C][C]diff[/C][C]lwr[/C][C]upr[/C][C]p adj[/C][/ROW]
[ROW][C]1-0[/C][C]-0.168[/C][C]-0.349[/C][C]0.013[/C][C]0.069[/C][/ROW]
[ROW][C]1-0[/C][C]0.039[/C][C]-0.077[/C][C]0.155[/C][C]0.51[/C][/ROW]
[ROW][C]1:0-0:0[/C][C]-0.15[/C][C]-0.427[/C][C]0.127[/C][C]0.497[/C][/ROW]
[ROW][C]0:1-0:0[/C][C]0.043[/C][C]-0.118[/C][C]0.204[/C][C]0.899[/C][/ROW]
[ROW][C]1:1-0:0[/C][C]-0.15[/C][C]-0.625[/C][C]0.325[/C][C]0.844[/C][/ROW]
[ROW][C]0:1-1:0[/C][C]0.193[/C][C]-0.092[/C][C]0.478[/C][C]0.296[/C][/ROW]
[ROW][C]1:1-1:0[/C][C]0[/C][C]-0.53[/C][C]0.53[/C][C]1[/C][/ROW]
[ROW][C]1:1-0:1[/C][C]-0.193[/C][C]-0.672[/C][C]0.286[/C][C]0.723[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203152&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203152&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Tukey Honest Significant Difference Comparisons
	diff	lwr	upr	p adj
1-0	-0.168	-0.349	0.013	0.069
1-0	0.039	-0.077	0.155	0.51
1:0-0:0	-0.15	-0.427	0.127	0.497
0:1-0:0	0.043	-0.118	0.204	0.899
1:1-0:0	-0.15	-0.625	0.325	0.844
0:1-1:0	0.193	-0.092	0.478	0.296
1:1-1:0	0	-0.53	0.53	1
1:1-0:1	-0.193	-0.672	0.286	0.723

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	3	1.278	0.284
	150

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 3 & 1.278 & 0.284 \tabularnewline
  & 150 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203152&T=4

[TABLE]
[ROW][C]Levenes Test for Homogeneity of Variance[/C][/ROW]
[ROW][C] [/C][C]Df[/C][C]F value[/C][C]Pr(>F)[/C][/ROW]
[ROW][C]Group[/C][C]3[/C][C]1.278[/C][C]0.284[/C][/ROW]
[ROW][C] [/C][C]150[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203152&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203152&T=4

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Levenes Test for Homogeneity of Variance
	Df	F value	Pr(>F)
Group	3	1.278	0.284
	150

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 2 ; par3 = Exact Pearson Chi-Squared by Simulation ;

Parameters (R input):

par1 = 1 ; par2 = 2 ; par3 = 3 ; par4 = TRUE ;

R code (references can be found in the software module):

cat1 <- as.numeric(par1) #
cat2<- as.numeric(par2) #
cat3 <- as.numeric(par3)
intercept<-as.logical(par4)
x <- t(x)
x1<-as.numeric(x[,cat1])
f1<-as.character(x[,cat2])
f2 <- as.character(x[,cat3])
xdf<-data.frame(x1,f1, f2)
(V1<-dimnames(y)[[1]][cat1])
(V2<-dimnames(y)[[1]][cat2])
(V3 <-dimnames(y)[[1]][cat3])
names(xdf)<-c('Response', 'Treatment_A', 'Treatment_B')
if(intercept == FALSE) (lmxdf<-lm(Response ~ Treatment_A * Treatment_B- 1, data = xdf) ) else (lmxdf<-lm(Response ~ Treatment_A * Treatment_B, data = xdf) )
(aov.xdf<-aov(lmxdf) )
(anova.xdf<-anova(lmxdf) )
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ANOVA Model', length(lmxdf$coefficients)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, lmxdf$call['formula'],length(lmxdf$coefficients)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'means',,TRUE)
for(i in 1:length(lmxdf$coefficients)){
a<-table.element(a, round(lmxdf$coefficients[i], digits=3),,FALSE)
}
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ANOVA Statistics', 5+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ',,TRUE)
a<-table.element(a, 'Df',,FALSE)
a<-table.element(a, 'Sum Sq',,FALSE)
a<-table.element(a, 'Mean Sq',,FALSE)
a<-table.element(a, 'F value',,FALSE)
a<-table.element(a, 'Pr(>F)',,FALSE)
a<-table.row.end(a)
for(i in 1 : length(rownames(anova.xdf))-1){
a<-table.row.start(a)
a<-table.element(a,rownames(anova.xdf)[i] ,,TRUE)
a<-table.element(a, anova.xdf$Df[1],,FALSE)
a<-table.element(a, round(anova.xdf$'Sum Sq'[i], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Mean Sq'[i], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'F value'[i], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Pr(>F)'[i], digits=3),,FALSE)
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a, 'Residuals',,TRUE)
a<-table.element(a, anova.xdf$'Df'[i+1],,FALSE)
a<-table.element(a, round(anova.xdf$'Sum Sq'[i+1], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Mean Sq'[i+1], digits=3),,FALSE)
a<-table.element(a, ' ',,FALSE)
a<-table.element(a, ' ',,FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
bitmap(file='anovaplot.png')
boxplot(Response ~ Treatment_A + Treatment_B, data=xdf, xlab=V2, ylab=V1, main='Boxplots of ANOVA Groups')
dev.off()
bitmap(file='designplot.png')
xdf2 <- xdf # to preserve xdf make copy for function
names(xdf2) <- c(V1, V2, V3)
plot.design(xdf2, main='Design Plot of Group Means')
dev.off()
bitmap(file='interactionplot.png')
interaction.plot(xdf$Treatment_A, xdf$Treatment_B, xdf$Response, xlab=V2, ylab=V1, trace.label=V3, main='Possible Interactions Between Anova Groups')
dev.off()
if(intercept==TRUE){
thsd<-TukeyHSD(aov.xdf)
names(thsd) <- c(V2, V3, paste(V2, ':', V3, sep=''))
bitmap(file='TukeyHSDPlot.png')
layout(matrix(c(1,2,3,3), 2,2))
plot(thsd, las=1)
dev.off()
}
if(intercept==TRUE){
ntables<-length(names(thsd))
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Tukey Honest Significant Difference Comparisons', 5,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ', 1, TRUE)
for(i in 1:4){
a<-table.element(a,colnames(thsd[[1]])[i], 1, TRUE)
}
a<-table.row.end(a)
for(nt in 1:ntables){
for(i in 1:length(rownames(thsd[[nt]]))){
a<-table.row.start(a)
a<-table.element(a,rownames(thsd[[nt]])[i], 1, TRUE)
for(j in 1:4){
a<-table.element(a,round(thsd[[nt]][i,j], digits=3), 1, FALSE)
}
a<-table.row.end(a)
}
} # end nt
a<-table.end(a)
table.save(a,file='hsdtable.tab')
}#end if hsd tables
if(intercept==FALSE){
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'TukeyHSD Message', 1,TRUE)
a<-table.row.end(a)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Must Include Intercept to use Tukey Test ', 1, FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')
}
library(car)
lt.lmxdf<-levene.test(lmxdf)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Levenes Test for Homogeneity of Variance', 4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,' ', 1, TRUE)
for (i in 1:3){
a<-table.element(a,names(lt.lmxdf)[i], 1, FALSE)
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Group', 1, TRUE)
for (i in 1:3){
a<-table.element(a,round(lt.lmxdf[[i]][1], digits=3), 1, FALSE)
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,' ', 1, TRUE)
a<-table.element(a,lt.lmxdf[[1]][2], 1, FALSE)
a<-table.element(a,' ', 1, FALSE)
a<-table.element(a,' ', 1, FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')

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Input Parameters & R Code